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Pima Indians Diabetes

Pima Indians Diabetes

In this article, we use Kaggle'sPima Indians Diabetes. The Pima Indians are a group of Native Americans living in an area consisting of what is now central and southern Arizona. A variety of statistical methods are used here for predictions.

Context

This dataset is originally from the National Institute of Diabetes and Digestive and Kidney Diseases. The objective of the dataset is to diagnostically predict whether or not a patient has diabetes, based on certain diagnostic measurements included in the dataset. Several constraints were placed on the selection of these instances from a larger database. In particular, all patients here are females at least 21 years old of Pima Indian heritage.

Content

The datasets consist of several medical predictor variables and one target variable, Outcome. Predictor variables include the number of pregnancies the patient has had, their BMI, insulin level, age, and so on.

Feature Explanations
Pregnancies Number of times pregnant
Glucose Plasma glucose concentration a 2 hours in an oral glucose tolerance test
Blood Pressure Diastolic blood pressure (mm Hg)
Skin Thickness Triceps skinfold thickness (mm)
Insulin 2-Hour serum insulin (mu U/ml)
BMI Body mass index (weight in kg/(height in m)^2)
Diabetes Pedigree Function Diabetes pedigree function
Age Age (years)
Outcome Whether or not a patient has diabetes

Train and Test Sets

StratifiedKFold is a variation of k-fold which returns stratified folds: each set contains approximately the same percentage of samples of each target class as the complete set.

Modeling: Gradient Boosting Classifier

Gradient Boosting Classifier (GBC)optimizes a model in several stages using differentiable loss function. See sklearn.ensemble.GradientBoostingClassifier for more details.

Some of the metrics that we use here to mesure the accuracy: \begin{align} \text{Confusion Matrix} = \begin{bmatrix}T_p & F_p\\ F_n & T_n\end{bmatrix}. \end{align}

where $T_p$, $T_n$, $F_p$, and $F_n$ represent true positive, true negative, false positive, and false negative, respectively.

\begin{align} \text{Precision} &= \frac{T_{p}}{T_{p} + F_{p}},\\ \text{Recall} &= \frac{T_{p}}{T_{p} + F_{n}},\\ \text{F1} &= \frac{2 \times \text{Precision} \times \text{Recall}}{\text{Precision} + \text{Recall}}\\ \text{Balanced-Accuracy (bACC)} &= \frac{1}{2}\left( \frac{T_{p}}{T_{p} + F_{n}} + \frac{T_{n}}{T_{n} + F_{p}}\right ) \end{align}

The accuracy can be a misleading metric for imbalanced data sets. In these cases, a balanced accuracy (bACC) [4] is recommended that normalizes true positive and true negative predictions by the number of positive and negative samples, respectively, and divides their sum by two.

Gradient Boosting Classifier with Default Parameters

Gradient Boosting Classifier with the Best Parameters

In order to find the parameters for our model, we can sue RandomizedSearchCV. Here, we have defined a function Best_Parm to find the best parameters.

Since we have identified the best parameters for our modeling, we train another model using these parameters.

Gradient Boosting Classifier with the Best Parameters and Feature Ranking

Conclusions

In this article, we tuned a GBC model with the best parameres and selected fewer features as the best features. However, the model accuracy didn't improve from that of the initial model.

References

  1. Smith, J. W., Everhart, J. E., Dickson, W. C., Knowler, W. C., & Johannes, R. S. (1988). Using the ADAP Learning Algorithm to Forecast the Onset of Diabetes Mellitus. Proceedings of the Annual Symposium on Computer Application in Medical Care, 261–265.
  2. scikit-learn Gradient Boosting Classifier
  3. Gradient Boosting Classifier Wikipedia page
  4. Mower, Jeffrey P. "PREP-Mt: predictive RNA editor for plant mitochondrial genes." BMC bioinformatics 6.1 (2005): 1-15.